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Flow behind an exponential shock wave in a rotational axisymmetric perfect gas with magnetic field and variable density

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ABSTRACT

A self-similar model for one-dimensional unsteady isothermal and adiabatic flows behind a strong exponential shock wave driven out by a cylindrical piston moving with time according to an exponential law in an ideal gas in the presence of azimuthal magnetic field and variable density is discussed in a rotating atmosphere. The ambient medium is assumed to possess radial, axial and azimuthal component of fluid velocities. The initial density, the fluid velocities and magnetic field of the ambient medium are assumed to be varying with time according to an exponential law. The gas is taken to be non-viscous having infinite electrical conductivity. Solutions are obtained, in both the cases, when the flow between the shock and the piston is isothermal or adiabatic by taking into account the components of vorticity vector. The effects of the variation of the initial density index, adiabatic exponent of the gas and the Alfven-Mach number on the flow-field behind the shock wave are investigated. It is found that the presence of the magnetic field have decaying effects on the shock wave. Also, it is observed that the effect of an increase in the magnetic field strength is more impressive in the case of adiabatic flow than in the case of isothermal flow. The assumption of zero temperature gradient brings a profound change in the density, non-dimensional azimuthal and axial components of vorticity vector distributions in comparison to those in the case of adiabatic flow. A comparison is made between isothermal and adiabatic flows. It is obtained that an increase in the initial density variation index, adiabatic exponent and strength of the magnetic field decrease the shock strength.

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Variation of the reduced flow variables in the region behind the shock front for ; ;  (non-rotating with constant density),  (rotating with variable density): a isothermal flow, b adiabatic flow: 1. radial component of fluid velocity , 2. density , 3. pressure
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Fig3: Variation of the reduced flow variables in the region behind the shock front for ; ; (non-rotating with constant density), (rotating with variable density): a isothermal flow, b adiabatic flow: 1. radial component of fluid velocity , 2. density , 3. pressure

Mentions: In non-magnetic case with constant density (i.e. , = constant) our solution corresponds to the solution obtained by Rao and Ramana (1976) (Vishwakarma and Nath 2007 in the case of perfect gas for cylindrical symmetry i. e. , ; Vishwakarma and Nath 2006 in dust free case for cylindrical symmetry i. e. for , ). To compare the obtained solution with the existing solution of Rao and Ramana (1976), the Fig. 3a, b are drawn in non-magnetic case. In Fig. 3a, b it is shown that the obtained solution is in good agreement with the existing solution of Rao and Ramana (1976). These figures demonstrate that the radial component of fluid velocity , density , pressure and the shock strength are decreasing for rotating medium than that in the case of non-rotating medium in the absence of magnetic field.Fig. 2


Flow behind an exponential shock wave in a rotational axisymmetric perfect gas with magnetic field and variable density
Variation of the reduced flow variables in the region behind the shock front for ; ;  (non-rotating with constant density),  (rotating with variable density): a isothermal flow, b adiabatic flow: 1. radial component of fluid velocity , 2. density , 3. pressure
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5016518&req=5

Fig3: Variation of the reduced flow variables in the region behind the shock front for ; ; (non-rotating with constant density), (rotating with variable density): a isothermal flow, b adiabatic flow: 1. radial component of fluid velocity , 2. density , 3. pressure
Mentions: In non-magnetic case with constant density (i.e. , = constant) our solution corresponds to the solution obtained by Rao and Ramana (1976) (Vishwakarma and Nath 2007 in the case of perfect gas for cylindrical symmetry i. e. , ; Vishwakarma and Nath 2006 in dust free case for cylindrical symmetry i. e. for , ). To compare the obtained solution with the existing solution of Rao and Ramana (1976), the Fig. 3a, b are drawn in non-magnetic case. In Fig. 3a, b it is shown that the obtained solution is in good agreement with the existing solution of Rao and Ramana (1976). These figures demonstrate that the radial component of fluid velocity , density , pressure and the shock strength are decreasing for rotating medium than that in the case of non-rotating medium in the absence of magnetic field.Fig. 2

View Article: PubMed Central - PubMed

ABSTRACT

A self-similar model for one-dimensional unsteady isothermal and adiabatic flows behind a strong exponential shock wave driven out by a cylindrical piston moving with time according to an exponential law in an ideal gas in the presence of azimuthal magnetic field and variable density is discussed in a rotating atmosphere. The ambient medium is assumed to possess radial, axial and azimuthal component of fluid velocities. The initial density, the fluid velocities and magnetic field of the ambient medium are assumed to be varying with time according to an exponential law. The gas is taken to be non-viscous having infinite electrical conductivity. Solutions are obtained, in both the cases, when the flow between the shock and the piston is isothermal or adiabatic by taking into account the components of vorticity vector. The effects of the variation of the initial density index, adiabatic exponent of the gas and the Alfven-Mach number on the flow-field behind the shock wave are investigated. It is found that the presence of the magnetic field have decaying effects on the shock wave. Also, it is observed that the effect of an increase in the magnetic field strength is more impressive in the case of adiabatic flow than in the case of isothermal flow. The assumption of zero temperature gradient brings a profound change in the density, non-dimensional azimuthal and axial components of vorticity vector distributions in comparison to those in the case of adiabatic flow. A comparison is made between isothermal and adiabatic flows. It is obtained that an increase in the initial density variation index, adiabatic exponent and strength of the magnetic field decrease the shock strength.

No MeSH data available.


Related in: MedlinePlus